Question: Solve for $x$ and $y$ using elimination. ${6x+4y = 56}$ ${5x-y = 38}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${6x+4y = 56}$ $20x-4y = 152$ Add the top and bottom equations together. $26x = 208$ $\dfrac{26x}{{26}} = \dfrac{208}{{26}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {6x+4y = 56}\thinspace$ to find $y$ ${6}{(8)}{ + 4y = 56}$ $48+4y = 56$ $48{-48} + 4y = 56{-48}$ $4y = 8$ $\dfrac{4y}{{4}} = \dfrac{8}{{4}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {5x-y = 38}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ - y = 38}$ ${y = 2}$